A paradox of vertebrate brain evolution is the unexplained variability in the size of the olfactory bulb (OB), in contrast to other brain regions, which scale predictably with brain size. Such variability appears to be the result of selection for olfactory function, yet there is no obvious concordance that would predict the causal relationship between OB size and behavior. This discordance may derive from assuming the primary function of olfaction is odorant discrimination and acuity. If instead the primary function of olfaction is navigation, i.e., predicting odorant distributions in time and space, variability in absolute OB size could be ascribed and explained by variability in navigational demand. This olfactory spatial hypothesis offers a single functional explanation to account for patterns of olfactory system scaling in vertebrates, the primacy of olfaction in spatial navigation, even in visual specialists, and proposes an evolutionary scenario to account for the convergence in olfactory structure and function across protostomes and deuterostomes. In addition, the unique percepts of olfaction may organize odorant information in a parallel map structure. This could have served as a scaffold for the evolution of the parallel map structure of the mammalian hippocampus, and possibly the arthropod mushroom body, and offers an explanation for similar flexible spatial navigation strategies in arthropods and vertebrates.sensory | memory | orientation | limbic